2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferencesover these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where xrepresents the number of cans of soda and y represents the number of juice boxes.a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y).b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda andjuice. Write Ping's demand curve for juice (y). Illustrate his demand curve.c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and$30, resp.). Use your demand functions to find his best bundle. In an indifference curvediagram illustrate his best bundle at these prices.For the remainder of the question assume that Ping's allowance (income) rises to $36 per week andthe prices of the two goods are unchanged at Px= $1.5 and Py= $1.d) Use your demand functions to find his new best bundle.e) Illustrate the new budget line and the new best bundle that you found above in your diagramfor part (c). Be sure to indicate the slopes of both budget lines.f) What is the income elasticity of soda (as a function of prices and income)?

Given Utility function U=0.5X+5logY where X=Soda Y=Juice Budget constraint M=Px.X+Py.Y

Answered: 2. Ping receives a weekly allowance to…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2Y/X and MUy = 2\X/Y ) a) Suppose Y=3. Calculate John's utility for X=4,9,16, and 25. For a given level of Y, does good X display diminishing marginal utility?
a. Determine the demand functions of x and y in the case of a Cobb-Douglas type utility function, in the following cases: α=0.40;β=0.60 Graph the demand functions of the two goods (price as a function of quantity) assuming the individual's income is $500 - Determine what is the quantity demanded of x and y, if the price of good x is USD 1, the price of good y is USD 4, and income is USD 500 - Now, explain what happens to the quantity demanded if the prices of the goods are doubles holding income constant.
The utility of a consumer derives from consuming the two goods X and Y can be assumed to be determined by the utility functionU(X,Y)= 4X03Y05. If good X costs 10 birr a unit and good Y costs 15 birr a unit and the consumer's income is 120 birr. What combination of X and Y that will maximize utility?
1. A consumer has the utility function U(x,y) = 2x y' where x and y represent the quantity consumed of goods X and Y. a) Find the consumer's marginal rate of substitution of X for Y. For parts (b) and (c) assume that the consumer has $100 to spend on goods X and Y which have fixed prices of px=1 and py=3. Use the Lagrangian method to solve the consumer's optimization problem: b) What are the first order conditions of the Lagrangian. Assume the solution to the consumer's optimization problem is c) interior. Solve for the consumer's optimal consumption bundle for any prices and income.
QUESTION ONE The only source of income available to Doreen, a level 200 student of UEW is her monthly stipend (M) from her parents. She neither saves nor borrows. Assuming she spends all her income on only two goods food (F) and Clothes (C), with Pr and Pc being the prices of the two goods respectively and having a utility function of the form: U = 6F°C i. Write an expression for Doreen's budget constraint. ii. Assuming good Fis on the vertical axis, produce a sketch of her budget constraint and determine the slope. iii. Find Doreen's monthly equilibrium demand functions for both goods. iv. With Pr and Pcgiven as ¢12 and ¢15 respectively and income of ¢300, calculate the equilibrium quantities of both goods. v. Compute the price elasticity of demand for both goods and interpret your results. vi. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of Food and Clothing.
Miss Coco consumes cheese cake and curry puff. Her consumption yields the following total utility as shown in the given table. Miss Coco has RM52 to spend. Suppose that the prices of cheese cake and curry puff are RM8 and RM4, respectively. Quantity (units) Total Utility Cheese Cake Curry Puff 1 56 32 2 104 60 3 136 84 4 160 104 5 170 116 6 176 126 7 178 134 What is the total utility received by Miss Coco at equilibrium?
Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?
10
Q1. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has income of $120; novels cost $5 each, while DVDs are priced at $15 each. a) Calculate Jason's optimal consumption bundle, AND his maximized utility level Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. b) In the same diagram, draw his old and new budget constraint; AND calculate his nep optimal bundle. c) Calculate the Total Effect (TE), Substitution Effect (SE) and Income Effect (E) of novels associated with the price increase of novels; AND SHOW them in your initial diagram. (Hint: keep 2 decimals if need)
Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3 S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. On the same graph, show the income and substitution effects of the increase in p from 1 to 2 on Rick’s consumption of Chicken McNuggets. Are Chicken McNuggets a normal or inferior good for Rick? Explain your answer.
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